The most commonplace example of the method of measuring velocity of a target by Doppler shift is probably the Doppler radar used by police departments to detect vehicles exceeding speed limits. Finding the discrete Fourier transform (DFT) of the demodulated Doppler radar returns separates the return into components falling into different frequency bins. The first moment of the power spectrum represents the Doppler frequency shift and the variance characterizes the spectral spreading; in completing the processing of the power spectrum the Doppler frequency shift and spectral spreading parameters can be converted to velocity measurements using the fundamental Doppler equation. This method is of interest in a number of other Doppler ranging systems, such as ones providing for the quantitative characterization of blood flow by Doppler ultrasound.
D. W. Baker describes the Doppler detection of pulsed ultrasound being used to map fluid flows in models and transcutaneously in the blood vessels of human beings in the paper "pulsed Ultrasonic Doppler Blood-flow sensing", IEEE Transactions on Sonics and Ultrasonics, Vol. SU-17, No. 3, July 1970, pp. 170-185. In medical ultrasound, many diagnostic procedures begin from the determination of the power spectrum of the returning signal. Certain of these diagnostic procedures, such as the quantitative characterization of blood flow by Doppler ultrasound, can provide better diagnostic precision if the power spectrum can be derived at the same sampling rate as that of the incoming signal. Attempting to do this real-time spectral analysis with a dedicated computer using known fast Fourier transform procedures has previously been inordinately expensive in terms of digital hardware and of the power consumption by that hardware, when attempting to meet speed requirements. Accordingly, the development of more refined medical diagnoses using ultrasound has been hampered.
The inventors describe dedicated hardware for performing fast Fourier transform in their U.S. Pat. No. 4,972,358 entitled "COMPUTATION OF DISCRETE FOURIER TRANSFORM USING RECURSIVE TECHNIQUES", issued Nov. 20, 1990 and incorporated in its entirety herein.